This is how you perform a like query in arel:
users = User.arel_table
User.where(users[:name].matches("%#{user_name}%"))
PS:
users = User.arel_table
query_string = "%#{params[query]}%"
param_matches_string = ->(param){
users[param].matches(query_string)
}
User.where(param_matches_string.(:name)\
.or(param_matches_string.(:description)))