Description of washing the beard during wudoo’ and ghusl
Question

                I have a medium length beard with empty patches on the sides. Do I have to rub it with water during wudu’ and ghusl, or it is enough to just wash it once by a fist of water while washing my face, just as the rest of the facial hair (eyebrows, moustache, and soul patch)?.
Praise be to Allah.Rubbing is mustahabb in 
    wudoo’ and ghusl according to most of the scholars, except for the 
    Maalikis. 
Al-Nawawi (may Allaah have 
    mercy on him) said in al-Majmoo’ (2/214):  
Our view is that rubbing 
    the parts of the body when doing ghusl and wudoo’ is Sunnah and is not 
    obligatory. If (a person) pours water over himself and makes it reach (the 
    skin) without his hands touching it, or he immerses himself in a large 
    amount of water, or stands beneath a downspout or in the rain with the 
    intention of doing ghusl, and it reaches his hair and skin, that is 
    sufficient for wudoo’ and ghusl. This is the view of all the scholars except 
    Maalik and al-Muzani, who stipulated that (rubbing is essential) in order 
    for ghusl and wudoo’ to be valid. End quote. 
Facial hair – including the 
    beard, moustache, tuft of hair beneath the lower lip (“soul patch”) and 
    eyebrows – is subject to further discussion. 
If it is thin and the skin 
    can clearly be seen beneath it, then it is obligatory to make the water 
    reach the bottom of it. If it is thick and the skin cannot be seen through 
    it, the outer surface only has to be washed, but it is mustahabb to run the 
    fingers through it. This applies in the case of wudoo’; when it comes to 
    ghusl, both the outer surface and lower layer must be washed. 
It says in Zaad 
    al-Mustaqni’: And he should wash his face from the hairline to the lower 
    edge of the beard and chin lengthwise, and from one ear to the other 
    crosswise, along with whatever thin hair may be present, and the outer 
    surface of thick hair and however far it extends. End quote. 
Shaykh Ibn ‘Uthaymeen (may 
    Allaah have mercy on him) said in his Sharh:
The words “along with 
    whatever thin hair may be present, and the outer surface of thick hair” 
    mean: that through which the skin is visible. Thick hair is that through 
    which nothing is visible. 
In the case of thin hair, 
    both it and what is beneath it must be washed. With regard to thick hair, 
    the outer surface, but not the inner layer, must be washed.  
Similarly it is essential 
    to wash whatever hair there is on the face, such as the moustache, “soul 
    patch”, eyelashes, eyebrows and sideburns. 
It is mustahabb to run the 
    fingers through thick hair, because the Messenger of Allaah  (peace and 
    blessings of Allaah be upon him) used to run his fingers through his beard 
    when doing wudoo’. 
End quote from al-Sharh 
    al-Mumti’ (1/212). 
It says in Fataawa 
    al-Lajnah al-Daa’imah (5/206): It is essential to wash the outer surface 
    of a thick beard, but it is not obligatory to wash the inner layers or the 
    skin beneath it, but it is prescribed to run the fingers through it. 
    Al-Nawawi (may Allaah have mercy on him) said: There is no difference of 
    opinion that it is obligatory to wash the thick beard, but it is not 
    obligatory to wash the inner layer of the beard or the skin beneath it, 
    according to scholarly consensus. This is the view of all the scholars among 
    the Sahaabah, Taabi’een and those who came after them. Ibn Rushd said: This 
    is something that is too well known for there to be any dispute. End quote. 
As for a thin beard through 
    which the skin may be seen, both the inner layer and outer surface must be 
    washed. End quote. 
And Allaah knows best.